Abstract
Peirce completed his work on graphical methods for reasoning within prepositional and predicate logic, but left unfinished similar systems for various modal logics. In the present paper, we put forward a system of Peircean graphs for reasoning within the modal logic S5. It is proved that our graph-based formulation of S5 is indeed equivalent to the traditional Hilbert-Frege formulation. Our choice of proof-rules for the system is proof-theoretically well motivated as the rules are graph-based analogues of Gentzen style rules as appropriate for S5. Compared to the system of Peircean graphs for S5 suggested in [17], our system has fewer rules (two instead of five), and moreover, the new rules seem more in line with the Peircean graph-rules for propositional logic.
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